Gauge protection in non-abelian lattice gauge theories
Gauge protection in non-abelian lattice gauge theories
复制标题
非阿贝尔晶格规范理论中的规范保护
DOI：
10.1088/1367-2630/ac5564
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发表时间：
2021
影响因子：
3.3
通讯作者：
P. Hauke
中科院分区：
文献类型：
--
作者：
Jad C. Halimeh;Haifeng Lang;P. Hauke
基于能量惩罚方案的格点规范理论的实验实现中规范不变性的保护最近在理论和量子合成物质的设置方面都激发了令人印象深刻的努力。一个主要的挑战是在非阿贝尔规范理论，局部守恒律不交换的这种计划的可靠性。在这里，我们表明，通过精确对角化（艾德），非阿贝尔规范不变性可以可靠地控制使用规范保护条款，大力稳定的目标规范部门在希尔伯特空间，抑制规范违规由于单一的规范破坏错误。我们提出的分析参数，预测体积独立的保护强度V，当足够大时，导致出现调整规范理论与相同的本地规范对称性，至少一个时间尺度<$V/V03。此后，重整化规范理论在时间尺度上占主导地位，其中V 0是体积无关的能量因子，类似于错误的阿贝尔规范理论的情况。此外，我们证明了某些实验相关的错误，单体保护项鲁棒地抑制规范违反所有可访问的演化时间在艾德，并证明了调整规范理论出现在这种情况下，以及。这些单体保护项可以很容易地实现，工程要求比理想规范理论本身更少，在当前的超冷原子设置和噪声中间尺度量子（NISQ）设备中。
Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization (ED) that non-abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength V, which when sufficiently large leads to the emergence of an adjusted gauge theory with the same local gauge symmetry up to least a timescale ∝V/V03 . Thereafter, a renormalized gauge theory dominates up to a timescale ∝exp(V/V 0)/V 0 with V 0 a volume-independent energy factor, similar to the case of faulty abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in ED, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and noisy intermediate-scale quantum (NISQ) devices.